Early this month, the top U.S. military officer was asked whether he thought Israel would alert the United States ahead of time if it attacked Iran’s nuclear program.

“I don’t know,” said Gen. Martin Dempsey, the new chairman of the Joint Chiefs, in a blunt assessment. In other words, our military is unsure whether our closest Mideast ally would give us advance notice of an act that could drag us into another Mideast war.

I’m aware that Dempsey’s remarks might have been a bit of psychological warfare. There’s the obvious advantage of giving us deniability. And there might be benefit to portraying Israel as beyond U.S. control.

It might give the Iranian regime pause if it believed Israel was getting ready to take matters into its own hands. And China might be more willing to endorse tough sanctions on Iran, as Washington has fruitlessly urged, if Beijing thought the alternative was an Israeli military attack.

Yet, there is something about Dempsey’s words that should make us uneasy. They exemplify a disturbing level of mistrust between Washington and Jerusalem that makes them ring true.

This mistrust is not, as Republican election campaign rhetoric would claim, a product of the administration’s failure to support Israel. On the contrary, defense cooperation between the two countries has never been closer. Moreover, President Barack Obama has twisted himself in knots to support Israel’s opposition to Palestinian statehood efforts at the United Nations.

Nor is the mistrust — on the surface, anyway — a product of public differences over approaching Iran’s nuclear program. After early attempts at engaging Iran failed, Obama adopted a tough stance toward Tehran, including harsh economic sanctions and diplomatic isolation. The president repeats at every opportunity that Iran will not be allowed to develop nuclear weapons and that all options (including military) are on the table.

Yet, as I witnessed at a fascinating, high-level dialogue in Washington between current and former Israeli and American officials, along with journalists and intellectuals, Israelis don’t believe Obama. At the eighth Saban Forum, sponsored by the Brookings Institution, I heard Israelis say repeatedly that Obama and his team were not credible when they said Iran wouldn’t be permitted to have nuclear weapons.

By the end of the forum, however, I was convinced that the issue isn’t so much credibility, as it is the Israeli conviction that the United States and Israel have a different take on the urgency of the threat.

Washington thinks the costs of a military strike on Iran would be so high that it shouldn’t be considered unless every other option is exhausted. Israel, on the other hand, thinks the Iran threat is immediate.

As Dempsey said, the United States believes sanctions and diplomatic pressure are the right path, while leaving open the possibility of future military action.

“I’m not sure the Israelis share our assessment (of how to handle Iran and its nuclear program),” the chairman told Reuters. “And because they don’t and because to them this is an existential threat, I think probably that it’s fair to say our expectations are different right now.”

In other words, the United States thinks there is still plenty of time to explore options other than military — although many Israelis don’t.

At the forum, Israeli participants expressed concern that a U.S. decision on using force would come too late, perhaps not until Iran publicly announces it is withdrawing from the Nuclear Nonproliferation Treaty and kicks out international inspectors. By that time, they worry, most of the program may be deep underground.

Yet the most salient point, I believe, was made by Secretary of Defense Leon E. Panetta, in the only forum address that was on the record. He pointed out that, at best, a military strike “might postpone (Iran’s nuclear program) maybe one, possibly two years.” It wouldn’t destroy, merely delay, Iran’s ability to produce an atomic weapon.

However, the “unintended consequences” of such a strike would be enormous, Panetta cautioned. Now isolated, Iran’s rulers would get renewed regional support. Prospects for regime change within the country would shrink. An oil price spike would undermine the fragile global economy, while rewarding the ayatollahs.

A military strike could precipitate another regional war at a time when the Mideast is already going through convulsions. It could embroil us in a new Mideast war, at a time when nuclear-armed Pakistan presents a greater danger to U.S. interests than Iran does. (Careless talk by Republican presidential candidates in support of hitting Tehran ignores the strategic implications of such an act.)

Israeli participants at the forum criticized Panetta for discussing the downside of an attack in public. Yet most of them also stressed that force must be the last option.

The forum — and my talks with individual participants — still left me with the impression that Israel might attack Iran without giving us advance notice — especially because Jerusalem fears Obama would say no.

Such an Israeli move would cost America dearly. Israel’s military capacity doesn’t match America’s, and the United States would be dragged into any military action. Moreover, we would inevitably be blamed for an Israeli strike, with Iran and its proxies striking back at U.S. interests in the Muslim world.

More to the point, the United States is Israel’s closest ally. For Jerusalem to ignore U.S. concerns and go it alone would be a betrayal of that friendship. Yet one can’t rule this prospect out.

I came away from the Saban Forum thinking how urgent it is that U.S. and Israeli officials do better at coordinating Iran strategy in private. And Israel must factor in American interests. Otherwise, one can envision disaster ahead.

• Rubin is a columnist and editorial-board member for the Philadelphia Inquirer.